Terahertz time-domain spectroscopy (THz-TDS) uniquely measures the absolute electric field transmitted through a disordered medium, and feedback optimization of the pattern illuminating an optical-rectification source has enabled the first field-level synthesis of single-cycle terahertz pulses at a chosen point behind a random medium — spatiotemporal focusing, absolute-phase (sign) inversion, and delay shifts over a range of a few picoseconds (Cecconi et al., ACS Photonics 2024). What remains open is the characterization and extension of the accessible waveform space of this scattering-mediated synthesis: the large-delay regime in which only a small number of transmitting modes carry significant group delay and transmission collapses; extension from a single target point to many simultaneous spatial targets with independently specified fields; more complex waveform specifications in larger, more strongly disordered media; and a predictive account, from measured medium parameters (mode count, transmission spectrum, near-field coupling, disorder strength), of which target waveforms are realizable and at what cost.

Background

A terahertz (THz) wave is electromagnetic radiation at frequencies of roughly 0.1–10 THz, between microwave and infrared. In THz time-domain spectroscopy (THz-TDS), an ultrashort laser pulse generates a single-cycle THz pulse — a pulse so short that it contains only one or two oscillations of the electric field — typically by optical rectification in a nonlinear crystal such as ZnTe, and a synchronized gating pulse measures the transmitted electric field E(t)E(t) directly, including its absolute phase, rather than only the intensity. This coherent, field-resolved detection is what distinguishes THz from visible-light experiments, where detectors are insensitive to the fast field oscillations and only intensities and relative spectral phases are accessible.

When such a broadband pulse propagates through a random (disordered) medium — e.g. a slab of packed scatterers — it is multiply scattered: the transmitted field is a coherent superposition of many randomly delayed and attenuated contributions, producing a speckled output that normally destroys the pulse. Wavefront shaping is the technique of pre-compensating the input so that the scattered contributions interfere constructively in a desired way at the output; it is typically implemented with a spatial light modulator (SLM), a programmable pixelated device that imposes a chosen phase or amplitude pattern on the beam. At optical frequencies, wavefront shaping has achieved focusing and compression of ultrashort pulses through scattering media (Katz et al., Nat. Photonics 2011), space–time control of transmission (Aulbach et al., Phys. Rev. Lett. 2011), and spatiotemporal coherent control via the multispectral transmission matrix — the measured set of input–output field relationships of the medium at many wavelengths (Mounaix et al., Phys. Rev. Lett. 2016). In the THz range, SLM-based wavefront shaping has mainly been used for single-pixel imaging of hidden objects (Stantchev et al., Sci. Adv. 2016). A transmission 'mode' here means an independent transmission channel of the scattering medium; only a subset of modes carries appreciable transmission, and each mode has its own group delay (the average arrival time of its energy).

Problem Statement

Characterize and extend the accessible field-level spatiotemporal waveform space of terahertz pulse synthesis through random scattering media, beyond the regime demonstrated by Cecconi et al. (ACS Photonics 2024). This objective comprises four open questions:

(i) Large-delay regime: quantitatively determine how the achievable delay range and the waveform fidelity of synthesized pulses depend on the medium's transmitting-mode statistics — in particular on the small subset of modes with large group delay and significant transmission — including the practical ceiling on delay imposed by the observed transmission collapse (most modes exhibit nearly zero transmission at large group delay, and total transmitted energy in the demonstrated configuration is around −40-40 dB).

(ii) Many simultaneous spatial targets: extend the demonstrated single-target-point field-level synthesis to many simultaneous spatial targets behind the same medium, each with an independently specified target field Etarget(t)E_{\mathrm{target}}(t) that may differ from target to target, and characterize the fidelity achievable per target as their number grows.

(iii) Richer waveforms and stronger disorder: extend the demonstrated waveform classes (spatiotemporal focus, absolute-phase inversion, delay shift) to more complex target field specifications, and establish whether field-level synthesis survives in larger and more strongly disordered samples where the transmitting-mode count and transmission fall further — distinguishing, in any claimed failure of synthesis, limits imposed by the medium itself from limitations of the particular optimization or detection route used.

(iv) Predictive account: replace purely feedback-optimized experimental search with a predictive framework that, from measured medium parameters (mode count and transmission spectrum, near-field source–medium coupling geometry — the sub-wavelength placement of the generation crystal relative to the scatterer, which determines which of the medium's modes are excited — disorder strength and sample thickness), determines which target waveforms are realizable and at what energy/fidelity cost — including explicit predictions for the delay–fidelity–transmission tradeoff of (i); such a prediction does not by itself resolve (i), which must be established by its own quantitative determination of the achievable delay range, the fidelity dependence on the mode statistics, and the practical delay ceiling.

References

  1. Vittorio Cecconi, Vivek Kumar, Jacopo Bertolotti, Luke Peters, Antonio Cutrona, Luana Olivieri, Alessia Pasquazi, Juan Sebastian Totero Gongora, Marco Peccianti, "Terahertz Spatiotemporal Wave Synthesis in Random Systems", ACS Photonics 11(2):362-368, 2024. DOI: 10.1021/acsphotonics.3c01671, https://doi.org/10.1021/acsphotonics.3c01671
  2. Vittorio Cecconi, Vivek Kumar, Alessia Pasquazi, Juan Sebastian Totero Gongora, Marco Peccianti, "Nonlinear field-control of terahertz waves in random media for spatiotemporal focusing", Open Research Europe 2:32, 2022. DOI: 10.12688/openreseurope.14508.1, https://doi.org/10.12688/openreseurope.14508.1
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